Question: Which of the following numbers is a multiple of 12? ${45,88,103,113,120}$
Explanation: The multiples of $12$ are $12$ $24$ $36$ $48$ ..... In general, any number that leaves no remainder when divided by $12$ is considered a multiple of $12$ We can start by dividing each of our answer choices by $12$ $45 \div 12 = 3\text{ R }9$ $88 \div 12 = 7\text{ R }4$ $103 \div 12 = 8\text{ R }7$ $113 \div 12 = 9\text{ R }5$ $120 \div 12 = 10$ The only answer choice that leaves no remainder after the division is $120$ $ 10$ $12$ $120$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $12$ are contained within the prime factors of $120$ $120 = 2\times2\times2\times3\times5 12 = 2\times2\times3$ Therefore the only multiple of $12$ out of our choices is $120$. We can say that $120$ is divisible by $12$.